OFFSET
3,1
COMMENTS
Let t(n) = (2n)!/(1!*2!*...*n!). Then t(n) is an integer for n = 1..5, and max{t(n), n >= 1} = t(4) = 140... . It appears that t(n) < 10^(-6) for n > 9.
EXAMPLE
338.9492801098942429745072350488697681125523042506474491612493021261451367444...
MAPLE
evalf(sum((2*n)!/product(k!, k=1..n), n=1..infinity), 120); # Vaclav Kotesovec, Oct 19 2014
MATHEMATICA
u = N[Sum[(2 n)!/Product[k!, {k, 1, n}], {n, 1, 300}], 120]
RealDigits[u] (* A248696 *)
NSum[(2 n)!/BarnesG[n+2], {n, 1, Infinity}, WorkingPrecision -> 103] // RealDigits // First (* Jean-François Alcover, Nov 19 2015 *)
PROG
(PARI) suminf(n=1, (2*n)!/prod(k=1, n, k!)) \\ Michel Marcus, Oct 19 2014
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 13 2014
EXTENSIONS
More digits from Jean-François Alcover, Nov 19 2015
STATUS
approved